I noticed that in my Notifications system preferences there two entries for Twitter (the old one with the white icon) and the new one.
The old Twitter application is long gone. How can I remove obsolete entries in the list?
I can't say for certain if this trick will work on older macOS versions, as I no longer have access to them. But, in High Sierra 10.13, you can just left-click once to highlight the offending entry, then tap the
<DEL> key (not backspace, forward-delete) to remove it.
I have two entries too, but they are not old and new. One is Twitter App, the other is system "build-in", this Twitter account for share(for example, click share button on Safari you can see it) and many other things.
You can check, "System Preferences"->"internet account".
If you click on the Help Center (?) icon (lower right of the Notifications pane), it says: To remove an app, drag it to the Not in Notification Center list.
Apps can be rearranged in the Notification Center by dragging them up / down in the list. 'Not in Notification Center' is at the bottom of the list. drag the app(s) you don't want to the very bottom, until you see a horizontal line appear beneath Not in Notification Center, then release. i'm not sure, however, if this will permanently remove the app from the list of apps in the Notification Center.